5 Types of Addition Strategies

Summary

In this educational video, Krystina introduces five strategies for solving addition problems, emphasizing their importance for building math skills. She warns against directly teaching these strategies to students, as they should emerge naturally from their understanding of numbers. The strategies include compensating, give and take, decomposing, breaking apart by place value, and the traditional algorithm. Krystina stresses the importance of number sense and place value in mastering these strategies, suggesting that teachers should encourage students to choose the best strategy for each problem rather than imposing a one-size-fits-all approach.

Takeaways

• 📚 The video discusses five strategies for solving addition problems, emphasizing that these should not be directly taught but should emerge naturally from students' understanding of numbers.
• ⚠️ Warning: The strategies discussed are not meant to be taught to all students universally, but rather to be aware of the different ways students might approach problems.
• 🔍 The strategies might be named differently by various educators, and the video encourages using names that reflect the mathematical concepts involved.
• 🧠 The strategies are based on students' number sense and understanding of place value, which are foundational for effectively using these strategies.
• 🔄 The strategies include compensating, give and take, decomposing, breaking apart by place value, and the traditional algorithm.
• 📈 The compensating strategy involves rounding numbers and then compensating for the difference, which helps in understanding the relationship between numbers.
• 🔄 The give and take strategy is similar to compensating but involves adjusting both numbers to make the addition easier.
• 📉 Decomposition involves breaking numbers into smaller, more manageable parts to facilitate addition.
• 🔢 The place value strategy involves breaking numbers into their place value components and adding them separately.
• 📘 The traditional algorithm is a systematic, step-by-step method taught in many educational systems for addition.
• 💡 The video stresses the importance of allowing students to choose the strategy that makes the most sense for the problem at hand, rather than prescribing a single method.

Q & A

What is the main focus of the video series introduced by Krystina?

The video series focuses on different strategies for solving addition problems, including time, measurement, and money addition, with the goal of building math minds in students.

Why does Krystina advise against directly teaching all five strategies to students?

Krystina advises against directly teaching all five strategies because students naturally use these strategies based on their understanding of numbers. Forcing them to learn all the strategies could cause confusion and doesn't allow for the organic development of number sense.

What is the 'compensating' strategy in solving addition problems?

The compensating strategy involves altering a number in a problem (e.g., rounding 399 to 400), solving the modified problem, and then adjusting the result to compensate for the change made initially.

How does the 'give and take' strategy differ from the 'compensating' strategy?

The 'give and take' strategy differs because instead of rounding a number, students shift part of one number to the other to make the numbers easier to work with. For example, a student might take 1 from 456 and add it to 399 to make 400 and 455.

What does Krystina mean by 'decomposing' in math addition?

Decomposing refers to breaking one of the numbers in the addition problem into smaller, more manageable parts, which are then added sequentially to simplify the process.

Why does Krystina prefer not to use number lines for the decomposing strategy?

Krystina prefers not to use number lines for the decomposing strategy because it is difficult to make the hops proportional, which can lead to confusion. Instead, she uses arrows or simpler methods.

What is the role of number sense in using these addition strategies?

Number sense is crucial because students must understand the relationships between numbers and how they interact. Without strong number sense and place value understanding, students will struggle to use these strategies effectively.

How is the 'place value' strategy used in addition?

In the place value strategy, students break down the numbers into their place values (hundreds, tens, and ones) and then add each place value separately before combining the sums.

What does Krystina mean by the traditional algorithm, and why does she not prioritize it?

The traditional algorithm refers to the step-by-step process of adding numbers by columns, carrying over when necessary. Krystina doesn’t prioritize it because it doesn't build number sense or place value understanding, as it can be done mechanically without deeper understanding.

What is Krystina's ultimate goal in teaching students these strategies?

Krystina's goal is to help students develop enough number sense and understanding of place value to choose the most appropriate strategy for each problem, rather than forcing them to use all strategies or rely solely on the traditional algorithm.

Outlines

00:00

📚 Introduction to Addition Strategies

The speaker introduces a series of videos aimed at explaining various addition strategies that students use. These strategies are not meant to be taught directly but are ways students might naturally approach solving addition problems, including those involving time measurement and money. The speaker, Krystina, warns that these strategies should not be directly taught to all students, as they may not be applicable in all situations. Additionally, the names for these strategies might vary, and the speaker emphasizes the importance of understanding the mathematical concepts behind the strategies rather than the specific names or methods of notation.

05:02

🔢 The Compensating and Give and Take Strategies

Krystina discusses two addition strategies: 'compensating' and 'give and take.' The compensating strategy involves rounding numbers to the nearest convenient number and then compensating for the difference. For example, adding 399 to 456 by rounding 399 to 400 and then subtracting one to adjust for the overestimation. The give and take strategy is similar but involves adjusting both numbers involved in the addition. The speaker uses the example of adding 9 and 7, where a student might adjust one number to make a more convenient sum, like rounding 9 up to 10 and adjusting the other number accordingly.

10:03

📈 Decomposition and Place Value Strategies

The speaker explains the 'decomposition' strategy, where students break down numbers into smaller, more manageable parts before adding them. This can be done using manipulatives like base ten blocks or by simply writing out the equation. The 'place value' strategy involves breaking numbers down by their place value (hundreds, tens, ones) and adding each place value separately before combining the results. Krystina emphasizes that these strategies require a strong understanding of number sense and place value, which are foundational to successfully applying these methods.

15:06

✅ The Traditional Algorithm and Encouraging Strategy Selection

Krystina describes the traditional algorithm for addition, which is a systematic approach taught in schools and involves carrying over values as necessary. She notes that while this method is reliable, it may not always be the most efficient or intuitive for students. The speaker advocates for building students' number sense and place value understanding so they can choose the most appropriate strategy for a given problem. The goal is not to have students solve every problem using all strategies but to recognize which strategy makes the most sense for a particular problem and to encourage their natural development of these strategies.

Keywords

💡Compensating

Compensating is a strategy where students adjust one number in an addition problem to make it easier to add, and then compensate for the change by subtracting or adding back the difference. In the video, this is illustrated by rounding 399 to 400 and then subtracting 1 to compensate, resulting in the correct sum of 855. This strategy helps students understand the relationship between numbers and how slight adjustments can simplify calculations.

💡Give and Take

Give and Take is a strategy where students adjust one of the addends by 'giving' or 'taking' a certain amount to make the numbers easier to add, and then adjusting the other addend accordingly. For example, in the video, a student might take 1 from 456 to make it 455 and add it to 399 to make it 400, simplifying the addition to 400 + 455 = 855. This strategy emphasizes the flexibility in number manipulation and the importance of keeping track of the adjustments made.

💡Decompose

Decompose refers to the strategy of breaking down numbers into smaller, more manageable parts to facilitate addition. In the video, this is demonstrated by breaking 456 into 400 + 50 + 6 and adding these parts to 399 in chunks. This strategy helps students develop a deeper understanding of numbers and their components, which is crucial for more complex mathematical operations.

💡Number Sense

Number Sense is the intuitive understanding of numbers and their relationships, which is essential for mathematical problem-solving. Throughout the video, number sense is highlighted as a foundational skill that enables students to effectively use addition strategies. For instance, understanding that 399 is close to 400 allows for the compensating strategy to be applied.

💡Place Value

Place Value is the concept that the value of a digit depends on its position within a number. The video emphasizes the importance of place value in strategies like breaking numbers apart by place value, where hundreds, tens, and ones are added separately before combining the results. This understanding is crucial for students to perform mental arithmetic and to apply various addition strategies.

💡Traditional Algorithm

The Traditional Algorithm, also known as the standard method of addition, involves aligning numbers by their place values and adding them from right to left, carrying over when the sum exceeds nine. The video discusses this method as a more rigid approach compared to the flexible strategies, and it is typically introduced to students once they have a strong foundation in number sense and place value.

💡Manipulatives

Manipulatives are physical objects used to represent mathematical concepts, such as base ten blocks, to help students visualize and understand mathematical operations. The video mentions manipulatives as a way for students to physically demonstrate their addition strategies, such as decomposing numbers into parts.

💡Number Line

A Number Line is a visual representation of numbers in a sequential order, which can be used to illustrate addition by showing the increments from one number to another. The video briefly touches on the use of a number line for the decomposing strategy, although it notes the difficulty in maintaining proportionality when using an iPad for demonstration.

💡Chunking

Chunking in the context of the video refers to the strategy of breaking down numbers into 'chunks' or groups that are easier to add. This is similar to decomposing but focuses on the process of grouping numbers in a way that simplifies the addition process, such as breaking 456 into 400 + 50 + 6.

💡Expanded Form

Expanded Form is a way of representing a number by showing the value of each digit according to its place value. In the video, this form is used to demonstrate the strategy of breaking apart numbers by place value, where each place value (hundreds, tens, ones) is added separately before summing up the totals.

Highlights

Introduction to a series of videos on addition strategies for students.

The five types of addition strategies will be explored to enhance math problem-solving.

Warning that these strategies should not be directly taught to all students.

Different names for strategies may exist, emphasizing the importance of understanding the math behind them.

Explanation that strategies manifest differently but remain fundamentally the same.

The 'compensating' strategy explained with an example.

The 'give and take' strategy, similar to compensating but with a different approach.

The 'decomposing' strategy involves breaking numbers into manageable chunks.

The importance of number sense in executing addition strategies effectively.

The 'breaking apart by place value' strategy, also known as the 'hundreds, tens, and ones' method.

The traditional algorithm for addition, its pros and cons.

The necessity of building number sense and place value before introducing the traditional algorithm.

Encouragement for students to choose the best strategy based on the problem at hand.

Advice for teachers to observe and discuss strategies rather than prescribing them.

The goal of the video series is to help teachers recognize and understand various addition strategies.

Final thoughts on the importance of allowing students to naturally develop their own strategies.

Transcripts

well with textbooks having students use

different strategies to solve addition

problems I wanted to do a short series

of videos to share with you what those

strategies are and how they help kids

not only do normal addition problems but

also time measurement and money addition

problems I'm Krystina ton of old they're

recovering traditionalist and today we

are going to do the first video in this

series that will take a look at the five

types of addition strategies in our

quest to build our math minds so we can

build the math minds of our students now

a couple of warnings I guess before we

get started number one I'm going to talk

about these strategies but they are not

strategies that you should directly

teach to all of your students

I want you to be aware of these

strategies because these are possible

ways that students think about solving

addition problems but we should not be

directly teaching them to our students

there are certain times when they will

use them in certain times that they

won't it's not like kids need to use all

five of these to solve any addition

problem they ever encounter now the

second warning is that you might call

them by different names you might have

different names for these strategies

when I first started doing this in my

classroom when a student would use this

strategy we would name it after the

student this is Sierra strategy is in

this awesome the way that Sierra solved

this one of the Articles that I read in

the teaching children's mathematics

which is published by NCTM I can't

remember the title of it it can't member

the who authored it but I remember the

gist of the article was that we should

stop naming them these cute names and

really name them after the mathematics

that is happening so I'm gonna be using

names that I use to talk about the math

that we are doing in the strategy you

might call them something different but

these are the names that I personally

use for them now the other thing I want

you to be aware of

is that to me there are five distinct

strategies you might end up seeing kids

who will combine or have variations on

these strategies but these are the main

basis of the five strategies and as my

dog wants to make an appearance so just

a moment I'll be right back

and so one of the things that actually

ends up happening is that we will see

these strategies but in different

formats like a kid might use the same

strategy but they were doing it using

base ten blocks whereas another kid just

wrote out the equation so just because

they're using manipulatives or an

equation or a number line to show their

strategy does not make it a different

strategy they're using a different model

to show that strategy so how they notate

it does not determine the strategy we

need to be paying attention to what is

the mathematics that they are doing for

this problem it doesn't matter how

they're showing that mathematics the

strategy is based upon how what they are

doing with the numbers and what's the

root of the mathematics all right so

let's dig in to those five types of

addition strategies okay we're going to

start with the strategy I like to call

compensating and for all of these we're

gonna use the same problem 399 + 456 and

I like to call this one compensating

because to me compensating is when you

do something you're not supposed to do

and you need to compensate for it

so the 399 this is when you will see

kids say well like that's almost 400 so

if I just add 400 to 456 that would be

856 but you weren't supposed to add 400

so we need to compensate for what we did

so this strategy only works if kids

understand the relationship between the

numbers that are in this problem and how

they've changed the problem so they need

to look at that and understand that they

added one more than they were supposed

to so they need to come at the end and

subtract one of those a way to get to

their answer of 855 now all of these

strategies the reason I love these

strategies is that they work no matter

what kind of addition problem you are

working with

so even when kids are learning just

their basic facts you will see kids who

will do these strategies you'll hear

kids say well nine plus seven that's

like having ten plus seven which is 17

and then I just need to take away one to

get to the sixteen and then it can

extend even further into work with

decimals and so on so the reason that I

love helping kids develop these

strategies is that they last kids beyond

just what they're doing with that one

problem when they really understand how

numbers work they will use these

strategies no matter what size of

numbers they are working with okay one

that is really similar to compensating

is one that I call give and take so it's

the kids who want to use 400 because

they see that that would be nice but

instead of just rounding it to the 400

they decided I'm gonna take one from the

456 and give it to the 399 so that I

have 400 but then I'm only left with 455

in that space now so it goes directly

they can get directly to their answer

after they have kind of done this

adjustment so they're still moving

things around but they do all of the

adjustments before they go to actually

solve the problem so with our young kids

that might look like this with the nine

plus seven you might see a kid who says

well I'm gonna take one from the seven

and give it to the nine so I've got ten

and then I've got six left over so 10

plus 6 gives me the 16 so again these

are really related but it's like what

are they seeing as the relationships how

are they going about the problem so

that's what really makes a difference

between the two strategies another

strategy that kids will devise is that

they will see that 456 and they'll say I

don't want to

all at once they will want to break it

apart into chunks that make sense for

them and this is what I call decomposing

because it's just like decomposing in

science it's a breaking it down into

smaller pieces so you might see a kid

who this might show up like on a number

line they might show it on a number line

I don't really like to show this one on

a number line because it's hard to be

proportional so I'm doing this on an

iPad so don't judge me if my hops are

not totally proportional I know they

should be but you might see a kid who

says I want to do add one here because

it's going to get me to the 400 sounds

similar to what we've been doing already

in these other strategies right but it

looks a little bit different from this

point on is that once they get there

then you might see a kid who goes okay

now I'm gonna add 400 I'm gonna do a big

chunk of it and then I'm gonna add a 50

right but the hard part here is that

they need to know how much they've added

they have to keep in mind that they need

to add the entire 456 but they can do it

in chunks but they have to keep track of

what those chunks have added up to so

along the way they need to be holding in

their head that they've done 450 and 1

and then think about how much more do

they need right they need to know once

they've done 451 how much more is that -

456 so they need to know that there's

five more see there's no my hop four

five looks the same as hot 450 and then

they would get to 855 okay so there's a

lot of number sense that goes into play

here they need a lot of knowledge about

how these numbers work the general idea

is that they are keeping one of the

numbers the same the 399 and then

they're breaking apart the other number

into smaller chunks and that doesn't

matter if they do it on a number line or

one of my favorite ways to show this is

just using arrows to show what I am

doing so that I don't have to worry

about being proportional so I'm gonna do

399 I'm just doing a little arrow I'm

not using the equal sign because you can

get this big mathematical run-on

sentences what I like to call it so I

just use arrows instead of equal signs

here so I've got 399 + 1 gets me to the

400

and then I'm going to add another 400

gets me to 800 and then maybe this time

I might add the 55 all at once it

doesn't matter what their chunks look

like as long as the general idea is that

they're breaking one of the numbers down

into chunks to make it friendlier to add

again it doesn't matter if they do that

on a number line or they show it with

these arrows or they make different

equations for every single step that

they do the idea is that they're just

breaking it down into smaller chunks to

make it friendlier to add kids will do

this same thing with like 9 plus 7 right

they might do 9 add 1 gets me to 10 adds

that add the 6 gets me to 16 now this

looks a lot like give-and-take

but it's because there's not a whole lot

of ways to break up the 7 right you may

even see a kid who maybe can't add the 6

all at once so they add one more and

they get to 11 they add one more they

get to 12 and so on it goes they just

add one by one by one alright that's the

extreme form of decomposing is doing it

one by one by one but even with these

upper amounts you might see a kid here

at that 400 stage they might not be able

to add the 400 all at once they may add

100 then another hundred then another

hundred then another hundred right the

ideas they're breaking it down into

friendly chunks that are friendly for

them alright another strategy that where

kids are breaking apart numbers is where

they break apart by place value some

textbooks will call this the hundreds

tens in one strategy I don't really like

that strategy because it limits kids to

thinking they can only do it with

hundreds tens and ones when they get

into decimals I want them to still be

able to use this strategy the general

idea is that they're breaking it down

and they are adding the the values

together in each place value and then

they're putting those together so some

of you may see this as expanded form so

sometimes it doesn't again it doesn't

matter how you model it it is the idea

of what's the mathematics that we are

doing I'm going to do a really shortened

version of this here and you could have

it out in expanded form but we're doing

the same thing the idea is that I'm

adding my hundreds together I have three

and 400 that gives me 700 I add my tens

together 90 plus 50 is a hundred and

forty and oftentimes what you'll hear

kids do right here is they'll be

thinking off to the side here that

that's already 840 then when they add

their ones they get the 15 whoops and

then they can add that to the 840 and

they get their 855 right all they're

doing is adding the chunks by place

value and this kids will naturally do if

they have a lot of work with place value

all of these strategies are dependent

upon number sense and place value you

cannot directly teach it if kids don't

already have a foundation of number

sense and place value now these are

things that we go really deep into in my

number sense courses but I'll also link

to some free videos that I have about

the basics of number sense so that you

can get a foundation of where to start

with your kids because if they don't

have these ideas they'll never be able

to really latch on to these strategies

now with 9 plus 7 you don't really have

a place value strategy because there

aren't any other place values you just

add your ones and your ones when we get

into things like 19 + 17 then you've got

some place values to work with and then

they'll add their tens with their tens

and their ones with their ones but

before that there's no real place values

to have to work with here alright our

last one is the traditional algorithm or

what in the United States we call the

traditional algorithm this is the way

that we traditionally learned how to

solve addition problems set it up and we

add our ones and then we carry it over

add our tens carry that over and then

we've got our answer now it's called an

algorithm because you can program a

computer a calculator to do it it is the

same steps every single time there's no

real decision-making to have to do here

you don't need number sense you don't

even have to have place value here all

you have to do is single-digit addition

and then be able to carry the one over

and carry the one over there's no

real judgment that has to go into this

which is one of the reasons why we use

it you do the same steps over and over

again and it works every single time but

it is devoid of place value and it's a

devoid of number sense unless we bring

that in as teachers that's why in most

states the standards bring in the

traditional algorithm at 4th grade

before that time we need to be building

their number sense and their place value

to help them be able to see and build

those other strategies that we've talked

about we want kids to be able to look at

a problem and decide the best way to

solve it because sometimes the

traditional algorithm yes it works but

sometimes it takes longer to solve the

problem using the traditional algorithm

than one of those other strategies so

the main idea from these videos what I

want you to really take away from it is

yes there are five different ways to

solve an addition problem but we do not

need to be making kids solve this one

problem five different ways we need them

to be able to look at the problem and

then decide for themselves what's the

best way to solve this problem what

makes sense because what makes sense for

this problem the 399 + 456 is different

then what should make sense for the

problem 323 + 456 how we solve these two

problems should be different

we should not approach them the same way

this one with the 399 is just begging me

to round that to a 400 or make that a

400 nothing in the 323 + 456 says round

this do compensating or give-and-take

but yet we could make kids do it we

could make them solve it that way but it

doesn't make sense - we want them to

have these strategies at their disposal

if it makes sense on that problem and

the only way that we help kids be able

to do that is by building their number

sense in place value so that they can

look at the problem first and say what

makes sense with this problem so

remember that these five strategies are

not things that you should directly

teaching to your students kids naturally

do these strategies based upon their

understanding of the numbers that are in

the problem we cannot directly teach

these strategies to students it comes

when they see relationships within the

numbers and they say oh I see how I

could use this and do this with it we

can't directly teach it even though our

textbooks try to that's why you will

spend weeks and weeks trying to get them

to use these strategies and by the end

of it all you really get our students

who are thoroughly confused ok I want

you to be aware of these strategies and

be watching for kids who are naturally

doing these and then have them talk

about and discuss what they're doing

instead of you directly telling them how

to solve using these strategies so this

video was to help you see the possible

ways that kids could solve addition

problems not that they have to solve

every problem five different ways I just

want you to be aware of these different

ways because if you were at all like me

back when I first started teaching the

only way I knew how to do it was the

traditional algorithm and when kids

solved it a different way I really had

no clue what they were doing I could not

tell what they were doing and I would

just say and don't do it that way do it

this way and I would tell them this way

to do the traditional algorithm the ways

that kids are solving these are

important pieces but they needed to be

coming naturally from them not us

directly teaching them so I want you to

be aware of them so that you can be

watching for them and pull them out when

you see kids using them all right I hope

that this video helped you build your

math mind so you can go build the math

minds of your students have a great day